Question

An evacuated spherical diving bell containing a camera is in the ocean at a depth of 145 m. It has a flat, transparent, circular port with a diameter of 17.1 cm. Find the magnitude of the total force exerted by the seawater on the port. For the density of seawater use 1025 kg/m3.

Calculate the total pressure at the given depth by adding up the atmospheric pressure (1.01e5 N/m2) plus the pressure due to the sea water. Evacuated means that that there is no air in the bell.

Answer 1

Step-by-step explanation:

pressure at the 145 m depth = atmospheric pressure + pressure due to depth of seawater = 1.01 × 10⁵ N/m² + ρgh where ρ is density of sea water = 1025 kg/m3, g = 9.8 m/s² and depth h = 145 m

pressure at the 145 m depth = 1.01 × 10⁵ N/m² + 14.57 × 10⁵ N/m² = 15.58 × 10⁵ N/m²

total pressure = F / A

F = total pressure × A

A area = πr² = 3.142 × 0.0855² = 0.02297 m²

F = 15.58 × 10⁵ N/m² ×0.02297 m² = 3.58 × 10⁴ N